1. Dynamics and Space Learning Intention You will be able to:
Analyse speed-time graphs to describe motion for objects to say if they are speeding up, slowing down, stationary or moving with a constant speed.
Calculate the distance an object has travelled from a speed time graph.

2. SPEED – TIME GRAPHS   
For any moving object it is possible to show how its speed changes with time by graphing the speed against the time for the journey. Three types of motion will be investigated:
Speeding up (called positive acceleration) Let’s go!
Constant speed
Slowing down (called negative acceleration)

3. Here is the graph of an object that is speeding up (positive acceleration):

4. Here is the graph of an object that is travelling at constant speed:

5. Here is the graph of an object that is slowing down (negative acceleration):

6. Copy the following graph of a car test run into your jotter and then describe the motion of the car, using the phrases “constant speed”, “speeding up” and “slowing down” during the 30 seconds of the test.

7. CALCULATING DISRANCES FROM GRAPHS 
You will find out how to calculate the distance travelled by an object. This may seem to be an easy task but it is not so easy when the object is speeding up or slowing down.   
If given a speed – time graph
Why does the distance travelled equals the area under the graph?

8. Look at the Rectangle below.
Breadth
Length
Area = Length x Breadth

9. Now calculate the distance travelled from the information in the graph below.
distance = speed x time Area = breadth x length
distance = x 3 Area = x 3
distance = 27 m Area = 27 m
Your teacher will show you the units are in metres.

10. Now find the distance travelled in the following car’s test run.
Area A
Area B
Area C
distance travelled = area under the graph
= Area A + Area B + Area C
= ½ bh bh ½ bh
= ½ x 4 x x 16 + ½ x 3 x 16 =
distance travelled = 136 m

11. 1 Calculate the distance gone by the cyclist from this speed-time graph.

12. 2 To test the strength of a nuclear waste container, the container is fired along a track towards a concrete wall. The speed-time graph is shown below.
a At what time did the container hit the wall?
b What speed was it travelling at when it hit the wall?
c What distance did the container travel along the track before hitting the wall?

13. 3 A glider, cruising at 20 m/s goes into a shallow dive and increases its speed. The graph shows its motion starting a few seconds before its dive.
At what time did the dive start?
What was the time taken during the dive?
What was the acceleration during the dive?
How far did the glider travel during the dive?

14. 4 Draw the speed-time graph for the following test run of a car and from it calculate the distance travelled by the car in this time.
Car accelerates from rest to a speed of 20 m/s in 8 s.
Car continues at a steady speed for a further 12 s.
Car decelerates to a stop in 5 s.

15. 5 An object is dropped from rest out of a window near the top of a tall building and falls for 3 s before hitting the ground. Its speed just before hitting the ground is 30 m/s.
Draw a speed-time graph for its fall and calculate the distance fallen.

16. During the test run of a TACV (traced air-cushion vehicle) or “hover-train” its speed was recorded as shown in the following table:
Draw a graph of the train’s motion during the test run (use graph paper).
Calculate the total distance travelled during the test run.
Calculate the average speed during the test run.
Time in s 10 20 30 40 50 60
Speed in m/s 90

17. SQA General 2009 Q15.
An indoor kart track hosts a racing competition.
(a) Describe how to find the average speed of a kart for one complete lap of the track. You must state the measurements that are made and how they are used.
(b) The speed of a kart and driver is recorded from the start of the race. The kart starts from rest and accelerates uniformly until it reaches check point X. Its speed at X is 12 metres per second. The time taken to reach X is 4 seconds.
(i) Draw a speed-time graph for the motion of the kart from the start until it reaches check point X.
Units and numerical values must be shown on both axes.